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Properties

Label 5.23
Level 5
Weight 23
Dimension 20
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 46
Trace bound 0

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Defining parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 23 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(46\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{23}(\Gamma_1(5))\).

Total New Old
Modular forms 24 24 0
Cusp forms 20 20 0
Eisenstein series 4 4 0

Trace form

\( 20 q - 2050 q^{2} + 33900 q^{3} + 9244700 q^{5} + 589062840 q^{6} + 1362465500 q^{7} + 31407300 q^{8} + O(q^{10}) \) \( 20 q - 2050 q^{2} + 33900 q^{3} + 9244700 q^{5} + 589062840 q^{6} + 1362465500 q^{7} + 31407300 q^{8} + 114884283350 q^{10} - 460775602760 q^{11} + 1136441909400 q^{12} + 54269753300 q^{13} - 24654495466500 q^{15} + 29835752508920 q^{16} - 80253280723900 q^{17} + 137917904677650 q^{18} - 281060017332300 q^{20} + 756138528774840 q^{21} - 2061075391073600 q^{22} + 1037077325344700 q^{23} - 6024188341937500 q^{25} + 20500754953296340 q^{26} - 23547612400178400 q^{27} + 22469384311691800 q^{28} + 1528221795380400 q^{30} - 59168290183124360 q^{31} + 127576605707160200 q^{32} - 122885145767188200 q^{33} + 224577413509081100 q^{35} - 348709371976890180 q^{36} + 31771763586263300 q^{37} - 68022880653205800 q^{38} + 403961337357211500 q^{40} - 518888589735353960 q^{41} + 728599883644233600 q^{42} - 163206026567312500 q^{43} - 812661089423650200 q^{45} + 2090595710115853240 q^{46} - 10782982108995000100 q^{47} + 15247496629702309200 q^{48} - 8078650456023358750 q^{50} + 7268352163823471640 q^{51} + 2826488770744359500 q^{52} - 82939890610911100 q^{53} + 14189107457301693400 q^{55} - 94674126521462497200 q^{56} + 80350630161456715200 q^{57} - 26333125419451333200 q^{58} - 43071849552234107400 q^{60} - 72296245181313351560 q^{61} + 120680979733299507400 q^{62} + 314158920699662531100 q^{63} - 471520867281802859500 q^{65} - 104114207586576205920 q^{66} + 105096237952998469100 q^{67} + 735294984009591844900 q^{68} - 1313980138396285170600 q^{70} - 299210622937211161160 q^{71} + 1193251694195206455300 q^{72} + 1585106250629647387700 q^{73} - 3200376752972286172500 q^{75} - 1648005154805557532400 q^{76} + 1169094250036333555000 q^{77} + 7071853912406390877000 q^{78} - 8629082541547347956800 q^{80} - 7480897589005926496380 q^{81} + 11769708632027547246400 q^{82} + 6404832513243753049100 q^{83} - 8722855036862153005900 q^{85} - 20231265275759088200360 q^{86} + 16438509410840410780800 q^{87} + 31243481322538554405600 q^{88} - 46016375169680434910250 q^{90} - 10784863800020180499560 q^{91} + 16671223272652373192600 q^{92} + 54305587231450109239800 q^{93} - 52590464181255799548000 q^{95} - 37868336306980033971360 q^{96} + 25374399591630151298900 q^{97} + 100231868908012136669950 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{23}^{\mathrm{new}}(\Gamma_1(5))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
5.23.c \(\chi_{5}(2, \cdot)\) 5.23.c.a 20 2